1. Field of Invention
This invention relates generally to morphing structures, for example aero-structures and, more particularly, to adaptive morphing of aero-structures and other structures.
2. Background Art
This background will utilize by way of example, aero-structures to illustrate a representative need for adaptive deformation or morphing of a structure. However, these background examples are in no way intended to narrow the scope of the present invention.
As an example, during its flight regime, an aircraft's wing needs to accommodate two extreme conditions. During cruise its lift-to-drag ratio should be maximized in order to allow for the longest range.
At landing a significantly lower speed is required to bring the aircraft to a standstill within the length of the runway.
Adaptive structures can be used to enhance flight performance of aircraft. Nature can be an inspiration for engineers that need to design wings that perform equally well in the cruise and in the landing regime. Sweep, twist, dihedral and aspect ratio, a bird can change each of them in a split second to change its flight path, and what is more impressive, it hardly takes any effort and the mechanism is low in complexity. The reader can observe how the individual birds change their wing geometry to soar, hover, or maneuver.
Matching the performance of bird morphing in combination with a low weight/energy/complexity penalty has proven to be very challenging. An important reason for this is that changes in the wing architecture do not only impact aerodynamics but also have an effect on the weight, structural integrity, and manufacturability of the aircraft. By way of illustration, For the same set of requirements, the individual categories that form the entire design concept all have different takes on which aircraft geometry satisfies these requirements best. These individual outlooks are synthesized into a complete aircraft design. Morphing wing design is especially challenging because its multidisciplinary nature impacts each of the individual groups or categories directly. For example, a swing wing can be beneficial from an aerodynamic standpoint; however, it also comes with a weight penalty and requires a completely different structural arrangement, which impacts the production and stress engineering groups.
Most efforts to mimic wing morphing have concentrated on unmanned airvehicles (UAVs) as will be detailed herein. However, few of the morphing technologies have transferred to the civil realm of aviation. One of the prohibiting factors is the fact that the adaptive materials that are often employed in morphing structures are not FAR 23, 25, 27 or 29 certified.
There is a need for an adaptive structure that can be developed that relies on conventional aerospace materials, has low power consumption, has low complexity and can be easily integrated into aircraft structures to enable optimal performance in both the cruise and landing regime by changing the outer geometry of the wing.
When adaptivity is addressed in terms of aircraft structural deformation, it should be apparent what condition the wing adapts to and what stimulus is required to achieve good adaptation. For commercial aircraft there are two extreme circumstances that the wing needs to adapt to: (1) maximum lift coefficient during landing and (2) maximum lift-to-drag ratio during cruise. Extensive research has been targeted towards making wings that perform well in both realms resulting in particular geometric characteristics
An adaptive structure is defined as: A structure which uses highly integrated, normally load-bearing, adaptive materials to undergo a change in mechanical, thermal, optical, chemical, electrical, or magnetic properties as a function of a given stimulus. With respect to aircraft structures, a change in mechanical properties is often most desirable since it allows for the ability to deform wing or empennage structure, influencing aircraft performance. The given definition incorporates the use of adaptive materials (materials that change their physical state as a function of a given stimulus). The most commonly used adaptive materials that change their mechanical state (strain) are shape memory alloy (SMA) and piezoelectric materials. The characteristics of these two adaptive materials, have been incorporated in aerospace applications, and their are advantages with respect to conventional alternatives
Shape memory materials have the ability to return to their shape after being plastically deformed. The most commonly used shape memory materials are shape memory alloys (SMAs). The Nickel-Titanium based SMAs can be fabricated to almost any shape or form. Plastic deformation in shape memory alloys induces the martensitic atomic structure to deform significantly. By increasing the temperature of the material, the atomic structure changes to austenitic, thereby returning the material to its original shape. When the material is subsequently cooled, the geometry is maintained and the atomic structure becomes martensitic again. If the material is in a particular form (e.g. rod, wire, bar) and loaded by a force, work can be performed.
SMAs have the highest single-stroke work density of the adaptive structures. They can exhibit great strains and apply considerable force. However, they generally exhibit a large power draw due to energy dissipation and their hysteresis can amount to 38%. Moreover, their bandwidth is generally poor because of thermal saturation issues [5].
Examples of the use of SMA in an aircraft application can be found as substitutes for conventional actuators in subscale uninhabited aerial vehicles (UAVs). An investigation into the use of adaptive materials in morphing structures demonstrated the effective use of highly integrated SMA materials for leading and trailing edge deformation on a wind-tunnel model of a contemporary fighter. Several morphing wing concepts based on SMA tendon (wire) actuators were conceived. Although these designs accomplish large deformations the structure of multiple parts, hinges, and actuators is complex and occupies most of the internal wing volume.
Other adaptive materials are piezoelectric materials, which generate an electric potential in response to applied mechanical stress, called the direct piezoelectric effect. Because this effect is reversible, piezoelectric actuators can be used in both sensor and actuator applications. A common piezoelectric material is Lead Zirconate Titanate (PZT). This material has randomly distributed dipoles within a polycrystalline structure. Poling the material is done by creating a large through-the-thickness electric field, which orients all dipoles in that direction.
Piezoelectric materials have been used for many years in applications such as pressure transducers and smoke detectors. Actuator applications include fuel injectors and valve lifters. The first applications of piezoelectric actuators in flight control systems appeared in the early 1990s relying on directionally attached piezoelectric torque plates. These torque plates were demonstrated in missile fins, subsonic and supersonic twist-active wings, and twist-active rotor blades.
Over the past two decades piezoelectric actuator elements have been demonstrated to reduce overall flight-control-system weight on miniature UAVs. By integrating piezoelectric bender elements into the control surfaces themselves, power consumption and complexity could be greatly reduced while a much higher actuation bandwidth could be achieved.
Piezoelectric materials have a lower single-stroke work density than SMAs and generally a limited stroke and force capability. However, recent advances in actuator design have led to a more robust and competitive actuator which has successfully been used in uninhabited aerospace applications ranging from subsonic through supersonic. This new class of actuators relied on an additional axial load to decrease the effective inherent stiffness of the actuator element.
Comparing adaptive materials can be done based on their mechanical, electrical, and/or chemical properties. One of the most important properties for aircraft applications is the specific energy density, or the amount of mechanical work that can be performed by a single gram of adaptive material. The coupling efficiency, k2, at which input energy is converted into mechanical work is another important parameter because it relates to the amount of energy that is required to induce mechanical work. Practical values of energy density might be 10 to 100 times lower than presented.
It can be observed that the conducting polymer has the highest mass-specific energy density (23 J/g), closely followed by SMA (15 J/g). Although their energy densities are high, their low transfer efficiency requires a relatively large amount of energy to actuate these materials. In addition, the actuators are relatively slow. Piezoelectric materials can have much higher transfer efficiencies. The ceramics (which are often considered for aircraft application) have a transfer efficiency of η=52% and are relatively fast. However, their energy density is three orders of magnitude lower than that of SMA. Other well-performing adaptive materials are the electroactive polymers. The acrylic artificial muscle, for example, has mass-specific energy density of 3.4 J/g, a transfer efficiency around 60%, and is relatively fast.
During the last decades, the ratio between cruise speed and landing speed has increased for commercial passenger aircraft. Sweeping the wing backwards to increase the drag divergence Mach number has had an adverse effect on the low-speed lifting capability of the wing. To account for the high CL conditions during take-off and landing, wings are generally equipped with high lift devices (flaps and/or slats). FIG. 4 demonstrates how the wing lift coefficient is influenced by high-lift devices. The more exotic flap systems that also have fully aft-translating capability are generally only found on high subsonic aircraft with swept wings. Low-subsonic aircraft such as light sport aircraft (LSA) do not require such a complicated high-lift system because the cruise-to-landing speed ratio is lower and the wings are generally unswept. In addition, LSAs are highly cost sensitive, which makes the addition of a complicated high-lift device less attractive. These aircraft therefore employ simple flap systems such as a split or plain flap. Leading-edge high-lift devices are not found on lowsubsonic aircraft.
Although effective, the aerodynamic advantages of a high-lift system come at a price. At the leading edge, movable flaps or slats are the highest-(aerodynamically) loaded parts of the wing. This requires extremely stiff and strong components within the extend/retract mechanism, which generally results in a significant weight penalty. The flap system complicates the wing's trailing edge structure and introduces electrical systems in relatively thin parts of the wing. For aft translating flaps, flap tracks are required that penetrate the airflow during cruise and increase wing drag. Furthermore, the system adds weight to the wing and increases the cost of manufacturing. However, the performance improvements are historically considered to outweigh these penalties.
The thickness ratio of an airfoil is its maximum thickness (measured perpendicular to the chord line) divided by the chord of the airfoil. The thickness ratio is one of the parameters that determine the maximum lift an airfoil can generate. It also has an influence on the post-stall behavior of the airfoil.
A basic example of the influence of thickness on the pressure distribution is demonstrated in FIGS. 6A and 6B where 6% and 18% thick airfoils of otherwise similar geometry are compared. The pressure peak (in a negative sense) at the leading edge of the thin airfoil is much higher than for the thick airfoil. Consequently, the pressure gradient, dp/dx, for this airfoil is much steeper. The steep slope of the pressure gradient is an indication that the boundary layer will separate at a lower angle of attack than for the thick airfoil, giving rise to an abrupt drop in lift. A simple two-dimensional Euler code predicts a maximum lift coefficient of 1.0 for the NACA 0006 and 1.8 for the NACA 0018. The stall for a NACA 0006 results in an abrupt loss in lift while the NACA 0018 shows a more gradual decay. Furthermore, for the NACA 0018 Cl max occurs at α=20 while for the NACA 0006 this is at α=9
FIGS. 7A and 7B shows the maximum lift coefficients for a series of airfoils as a function of their thickness. Note in these graphs how Cl max is strongly influenced by the Reynolds number. Comparing Figures (a) and (b) shows the difference in maximum lift due to camber. The MS(1) airfoil shows distinctly better high lift characteristics than all the other airfoils but is much more susceptible to a change in Reynolds number (see FIGS. 6A and 6B for geometry).
The combination of airfoil thickness and flap type was shown to be instrumental in the maximum lift capabilities of an airfoil, as can be seen in FIG. 8. This graph displays the change in maximum lift coefficient for a relative flap chord of 25% and standard flap deflection angles. FIG. 8 shows that flap deflection is more effective on thick airfoils than on thin airfoils. Using advanced flap mechanisms (double slotted) in combination with a 19% thick airfoil can change the maximum lift coefficient as much as 1.9.
A second characteristic of the wing section geometry that is important in determining its maximum lift capability is its camber. As was already clear from FIGS. 7A and 7B, the more positive camber is present, the higher the lift that can be generated. On conventional transonic wings, the deployment of high lift devices increases the effective camber of the airfoil (see FIG. 4).
In the 1920s a morphing wing concept for a triplane was conceived. The middle wing relied on the local angle of attack to change its camber and consequently its maximum lift capability. This simple concept of passive wing morphing did not require pilot input but relied on a balance between the external aerodynamic forces and the internal spring force that dictated the shape of the airfoil. Even though the mechanism could work well, the structure lacks an integral torque box that is essential to provide appropriate levels of torsional stiffness.
Over the past three decades a renewed interest in wing morphing has sparked various research programs. Among these programs was the Mission Adaptive Wing (MAW) research program that investigated the effectiveness of variable leading and trailing edge camber on an F-111 aircraft. This wing had an internal mechanism to flex the outer wing skin and produce a symmetrical section for supersonic speeds, a supercritical section for transonic speeds, and a high-camber section for subsonic speeds. Flight tests demonstrated that an improvement in lift-to-drag ratio of 20% could be obtained in large parts of the flight envelope while some parts even showed an increase of 100%. Even though the flight tests demonstrated advantages of the wing morphing, there were significant drawbacks to the way the morphing was achieved. Bulky, heavy hydraulic screw jacks were employed to induce the deformation in the wing. In addition, internal mechanisms employing multiple linkages ensured the desired kinematics of the mechanism. This resulted in a relatively heavy and complex actuation system.
It has been recognized that wing morphing on stiff aircraft structures requires dedicated structural mechanisms and often compliant wing skins (such as in the MAW) that allow for these shape deformations. As a result, compliant mechanisms and compliant materials have been conceived that can be used in morphing wings. Although effective in providing significant wing deformations and smooth transitions, compliant mechanisms are often much more complicated than the control surfaces they are replacing.
The shape of the leading edge is a third parameter that influences the maximum lift capabilities of an airfoil. As was mentioned in the previous section, to achieve a maximum ΔCl max to change in camber, there exists an optimum Δy. For symmetric airfoils (no camber), FIG. 10 shows how the leading edge shape triggers the type of stall that occurs and its influence on the maximum lift coefficient. It shows that relatively sharp leading edges suffer from leading edge stall and have a low Cl max, while with incrementally more blunt airfoils, stall starts at the trailing edge and leads to higher lift coefficients. The (recirculation) “bubble” that is mentioned in this graph refers to the laminar separation bubble. This bubble occurs when the laminar boundary layer cannot follow the curvature of the airfoil, separates from it, becomes turbulent, and re-attaches to the airfoil again further downstream. At a certain angle of attack, the bubble bursts, no re-attachment occurs, and a sudden drop in lift results.
It was already shown in the 1950s that modification of the nose of a 35° swept wing could result in significant changes in maximum lift coefficient. Demele and Sutton demonstrated that by adding body to the bottom side of a NACA 64A-010 over the first 20% of the chord resulted in an increase in Cl max of 35% (at a Reynolds number of 11×106).
Closely related to the leading edge shape parameter, Δy, is the leading edge radius, R. FIG. 11 shows an example of how the radius influences the maximum lift coefficient. A NACA 64A-010 has a maximum lift coefficient of 1.07. Increasing leading edge droop resulted in an increase in maximum lift coefficient of 0.37. Increasing the radius from 1.10% c to 1.50% c yielded an additional increase in Cl max from 1.44 to 1.65 bringing the total increase to 0.58 or roughly 50% of the original maximum lift [65]. Efforts to increase the maximum lift coefficient on a NACA 63012 airfoil yielded similar results. A larger nose radius (increased from 1.09% c to 3.5% c) was introduced. In addition, keeping the nose radius tangent to the upper surface contour of the basic airfoil resulted in an increase in leading edge droop. These combined measures resulted in a ΔCl max=0.35 [66].
Increasing the nose radius reduces the local curvature of the airfoil which in turn lowers the leading edge pressure peak (see FIGS. 6A and 6B for comparison of sharp and blunt airfoils). Accordingly, the boundary layer is less likely to separate, which means a postponement of leading edge stall. All measures that are described above essentially aim to reduce the local over speeds at the leading edge. Apart from increasing the nose radius and adding body on the bottom side of the airfoil, other measures, such as adding body on the top side of the airfoil, also proved to be effective on other airfoils [67]. It depends on the contour of the basic airfoil which measure proves to be most effective in increasing the maximum lift coefficient.
Examples of leading edge morphing are often found in conjunction with thickness and camber adaptivity. This means that by changing the thickness or camber the leading edge geometry is also altered in a favorable manner Research has been done on helicopter blades to ensure attached flow on the retreating blade at high angles of attack (see FIG. 12). It was shown that by using a compliant mechanism inside the blade leading edge, the leading edge geometry could be altered on a 3-ft-span full-scale chord blade at a rate of 6 Hz.
Significant effort has been conducted in the realm of morphing flaps or ailerons. The benefit of continuously deforming flap is that there are no gaps or seams between individual wing components. This is beneficial during cruise operations because it decreases friction drag. Because adaptive flaps are integrally attached to the main wing, they do not benefit from the jet effect that exists when a flap is slotted. In addition, they lack any Fowler motion. Therefore, it is expected that maximum lift capability of an adaptive flap is not as high as that of any of the slotted or Fowler flaps of FIG. 4. However, the smooth transition between main wing and adaptive flap, makes it an excellent candidate for an adaptive control surface such as an adaptive aileron.
Another way of increasing the maximum lift capability of a wing is to apply a Gurney flap at the trailing edge. A Gurney flap is small vertical tab (generally not larger than 5% c) that makes a right angle with the pressure surface at the trailing edge of the wing. It creates a local increase in pressure which gives rise to a higher lift coefficient. It also induces a significant increase in pitching moment because of high aft loading. Different geometries of Gurney flaps have been investigated in terms of lift, drag and pitching moment characteristics. For example, a NACA 23012 airfoil at a Reynolds number of 1.95·106 experienced a maximum-lift increase of 49% (from 1.26 to 1.88) due to the application of a 5% c straight Gurney flap. Rather than applying the Gurney flap to the end of the airfoil, it can also be attached to the trailing edge of a flap. Application of a 1% c Gurney flap on 30% c Fowler flap resulted in an increase of 3% in Clmax at a flap angle of 39° [80]. A 5% c Gurney flap on a 2-element, single-slotted wing showed an increase in Clmax of 20% (from 1.70 to 2.05).
Another way of achieving wing deformation is by utilizing the aerodynamic loads that are already present. This can be beneficial because deformation of a wing structure generally requires considerable amounts of energy. Extracting this energy from the airstream rather than from actuators reduces the size and consequently the weight of the wing-movable. Research into these so-called active aeroelastic wings (AAWs) has resulted in successful flight tests of an F/A-18A that employed a flexible wing that demonstrated span-wise twist as a result of small leading and trailing edge control surface deflection. Although roll rates of the aircraft increased to 400 deg/s, a complex control mechanism was required to deflect the various control surfaces in order to obtain the required wing twist. In addition, the torsional rigidity of the wing was intentionally weakened which must have decreased the flutter and divergence clearance.
Other academic efforts that demonstrated the use of aero-elastic flight control include the use of adaptive internal structures. This concept relied on a change in wing stiffness to have the air loads induce wing twist. Both internal and external mechanisms relied effectively on the twisting of the wing to induce roll control.
Because aeroelastic active wings can be sensitive to adverse aero-elastic effects such as aileron reversal, static divergence, or flutter, research has been conducted to make morphing wings that rely on internal actuators for deformation. Driven by the knowledge that washout-adaptive wings can reduce induced drag as well as control the rolling motion, researchers have implemented a variety of twist active wings on (subscale) UAVs. An example is a UAV, which uses so-called twisterons that can be adjusted to decrease lift-induced drag during cruise. DARPA's smart materials and structures demonstration program explored the use of an SMA torque tube to twist the wing. The main drawback of twist-active wings is that there is should always be a trade-off between torsional stiffness on the one hand and actuator sizing on the other hand. In general, powerful (heavy) actuators are required to torque a structure that is designed to be torsionally stiff. One concept of active wing twist, however, relied on the warping of the skin to induce the torsional change. Because the skin warping was done by using a jack-screw, the torsional rigidity was not compromised and relatively light-weight actuators were required.
For a given airfoil (2D) shape, the thickness ratio (t/c) is often the most important parameter that influences the drag divergence Mach number. FIG. 14 shows how for supercritical and NACA airfoils the thickness ratio influences the drag-divergence Mach number. According to this graph, for supercritical airfoils, the drag-divergence Mach number decreases linearly according to MDD=0.92-1.16 (t/c). For example, decreasing the thickness of 10% thick airfoil down to 8% increases the drag-divergence Mach number from 0.80 to 0.83.
The drag divergence Mach number of a wing is typically a function of both the sweep of the wing and the thickness of the airfoil. The critical Mach number, M*, is the Mach number at the onset of supersonic flow locally on the wing. The critical Mach number and the drag divergence Mach number can be roughly correlated according to MDD=M*+0.1 [42]. By decreasing the airfoil thickness, the critical Mach number and hence the drag-divergence Mach number is decreased. FIG. 15 shows how the critical Mach number varies with thickness and sweep angle for a wing of aspect ratio larger than 6 and a lift coefficient of 0.4. From this graph it can be seen that in order to decrease the critical Mach number (and hence the drag-divergence Mach number) a trade off needs to be made between airfoil thickness and sweep angle. The influence of the sweep angle on the maximum lift coefficient is evident from Equation 2.3. It is therefore desired to keep the wing sweep as low as possible to maximize low-speed performance. Other disadvantages include (a) the added structural weight that is required to bear the torque load that is introduced by sweeping the wing, (b) reduced flap effectiveness, and (c) a spanwise drift over the wing that increases boundary layer thickness and leads to increased drag and reduced aileron effectiveness. Because of these disadvantages, decreasing airfoil thickness would be a beneficial solution. However, this leads to other inconveniences like added structural weight to bear the bending moment of the wing and less volume for fuel storage.
Since transonic aircraft cruise close to the drag-divergence Mach number (MDD≅Mcr) an example of the relation between sweep angle and Mach number for the aircraft is presented in FIG. 16. The direction of the arrow in this graph indicates that most efficient transonic wings both have low sweep angles and still cruise at relatively high Mach numbers. From this graph it becomes apparent that particularly the Fokker 70 employs a very efficient transonic wing design. Its wing is swept backwards over only 17 degrees and still its cruise Mach number is 0.77. Remember that this aircraft does not have any leading-edge high-lift devices to increase its maximum lift coefficient at take-off and landing, which demonstrates that the lack of sweep makes for better low-speed wing performance. An explanation for these performance characteristics is the relatively thin wing which measures only 12.3% at the root and 9.6% at the tip. For comparison, the wing of a B767-400 has a thickness of 15.7% at the root, 28% more than the Fokker 70.
Planform morphing is yet another form of wing shape deformation that allows an aircraft to expand its flight envelope and fly efficiently in both the high speed and low speed realm. An example of planform morphing was successfully demonstrated in 2006 on both a wind-tunnel model and a scaled prototype. Using a scissor-type mechanism this wing was capable of changing its span, planform area, aspect ratio and sweep angle. An elastic skin ensured a smooth wing surface at each stage of wing morphing. Even though the effectiveness of this wing was excellent, penalties in terms of complexity and the impossibility to store fuel become clear. In addition, the complex wing structure in combination with the requirement of powerful actuators led to a very high weight penalty.
Another approach to planform morphing used a hinged segmented wing that could fold partly against its fuselage, thereby decreasing the wing surface area and increasing the effective sweep angle. The design of this folding wing concept incorporated tailored seamless skins around the hinge points such that a smooth surface was ensured in all positions of the wing. By reducing the effective surface area when in folded position the intention was to reduce drag and be able to fly efficiently in the high speed realm. Wind tunnel tests successfully demonstrated the morphing mechanism, but were inconclusive about the expected drag reduction at transonic and supersonic speeds. It might be expected that interference-drag penalties occurring in folded position negate the drag reduction due to increased effective sweep and decreased wing area.
Continued efforts are being made to conceive new morphing concepts that could potentially be used in future aircraft designs. These efforts include research into new compliant mechanisms, adaptive materials, and aircraft configurations that enable morphing flight control. The majority of the research is tailored towards novel UAV designs and is often still in the conceptual stage of the design.
The overview of morphing projects in the past decades has been primarily targeted towards military applications, particularly UAVs. Passenger aircraft have to comply with strict rules and regulations (FARs) in terms of structures and materials. Therefore, morphing structures have been limited to the high lift devices such as flaps and slats. An example of wing morphing on passenger aircraft can be found on the (canceled) Boeing 2707 supersonic transport (SST), which was proposed in 1964 in response to the European Concorde. A swing-wing configuration similar to that of the F-111 (and later F-14) was used to change the wing sweep between subsonic and supersonic speeds. However, due to insurmountable weight problems associated with the swing-wing mechanism Boeing discarded this morphing concept in favor of a fixed delta wing. The project was cancelled before one prototype was built due to heavy opposition by (among others) environmentalists.
Since contemporary passenger aircraft rely on their efficiency in order to be cost effective, changes in structural arrangement are only justified when direct operating cost (DOC) is decreased and the structural integrity is not compromised. The morphing wing concepts which were conceived for military applications (e.g. F-111, F-14 and F-18 AAW) are therefore unsuitable for commercial applications. The Mission Adaptive Wing, the tendon actuated structure, and the variable planform wing are examples of complex internal structures that require large numbers of parts, hinges and actuators to work properly. Maintaining such structures can be costly and is, therefore, unattractive for commercial airliners. Other disadvantages such as the limited ability to store fuel in the wings or a complex control system have prevented morphing technology from transferring from the experimental military aircraft to modern transport aircraft. As was mentioned before, because adaptive materials have not been certified for use in primary or secondary aircraft structures, applying them on commercial aircraft is still impossible.
Commercial applications of morphing structures can only be viable if certifiable systems (including certifiable materials) are used, direct operating costs are decreased, and structural integrity is maintained. To satisfy these disparate requirements, a radically different approach is required. To be competitive with conventional high lift devices on modern jet transports this morphing wing should produce values of CLmax that are comparable to those presented FIG. 5. Furthermore, there is the objective to keep the number of parts, number of actuators and system complexity as low as possible. This enables a reduction in both manufacturing and maintenance cost. Finally, no weight, aerodynamic or aeroelastic penalties may arise as a result of the morphing concept.
The journey of a typical jet transport aircraft imposes different atmospheric conditions on the aircraft. Most jet transports cruise at altitudes between 10 and 13 kilometers, which means lower temperature, density, and pressure than at take-off and landing conditions. This section shows the temperature, pressure and density distribution in terms of latitude and altitude of the Earth's atmosphere in standard and deviated conditions.
In reality the atmosphere is never constant and standard atmospheric conditions are rarely encountered. The influence of seasons provides the first deviation from standard conditions. A second deviation comes from the position on Earth in terms of latitude. FIGS. 17A and 17B shows how the mean temperature varies with altitude and latitude. The difference between the isotherms in (a) and (b) shows that during winter the temperature distribution is more dependent on latitude than during summer. An aircraft flying over the tip of Greenland (60°N latitude) at an altitude of 10 km would therefore experience a temperature of 217K during winter and 226K during summer (on average).
In contrast to the global temperature distribution, FIGS. 18A and 18B demonstrates that the mean global pressure distribution is only mildly dependent on latitudinal and seasonal changes. The upper layers of the troposphere show a somewhat higher variability while near sea level the variations are almost negligible.
By using the mean temperatures and pressures and assuming that air behaves as a perfect gas the global density distribution can be calculated (using the perfect gas law, p=ρRT, and R=287 J/kg/K). The density distribution, which is presented in FIGS. 19A and 19B, demonstrates that near the surface the mean density in both winter and summer is dependent on latitude, while at higher altitudes the isochors show little latitudinal or seasonal variation. The isochors of FIGS. 19A and 19B are important for aircraft cruise and airfield performance because they directly relate to the amount of lift the wings can generate. The temperature on the other hand only plays a role in the cruise condition because it determines the local speed of sound, α=√{square root over (γRT)} (γ=1.4), and therefore the cruise velocity of the aircraft. The small seasonal and latitudinal variability in mean densities at altitudes between 10 and 15 km indicate that the cruise altitude for aircraft is fairly independent of place and time.
Contrary to cruise performance, airfield performance is dependent on the latitudinal position and seasonal time of the year. FIGS. 19A and 19B demonstrates that near sea level mean air densities increase with latitude and are higher in winter than in summer. A statistical relationship seems to exist between temperature and density. Lower densities imply that aircraft need longer take-off distances, not only because of less lift capability but also because of reduced engine thrust [1].
From the data presented in FIGS. 17A and 17B to FIGS. 19A and 19B the relation between temperature and density was investigated up to altitudes of 3 gpkm. This relation is shown in FIG. 20 for mean winter conditions. Investigating summer conditions resulted in a close match with the winter data, only over a smaller range of temperatures and was, therefore, not drawn in. The seasonal influence was negligible and data from latitudes between 10°S and 75°N was used. For this reason, it was anticipated that the temperature-density relation as presented in FIG. 20 was representative for global atmospheric conditions. Isobars were drawn to show the pressure-temperature relation according to the perfect gas law. It can be seen that at low altitudes (up to 1 gpkm) the density-temperature relation followed the shape of the isobars closely, resulting in good predictability of aircraft thrust and lift as a function of temperature only.
In addition to the standard deviation in temperature, the deviation in pressure was also investigated. Due to the fact that the pressure extremes during winter and summer were virtually the same as the average pressure distribution as shown in FIGS. 18A and 18B it is not presented in a separate figure. Due to the minimal pressure deviation, the extreme density was assumed to be a function of temperature only. The relationship between temperature and density on extremely cold days is shown in FIG. 22. As can be seen in FIG. 22, near sea level the density-temperature relation followed the isobars closely, while at higher altitudes the deviation was larger, although a higher correlation with isobars was present than for the mean winter temperatures. The same trends between density and temperature hold on extremely cold days as well as on extremely hot days throughout the range of latitudes shown in FIG. 21.